Revealing the nature of the electroweak phase transition (EWPT) is one of the most important tasks in particle physics after the discovery of the Higgs boson at the LHC [1]}, [2]}. In the Standard Model (SM), lattice calculations have shown that the EWPT is a smooth crossover [3]}, [4]}, [5]}. However, the EWPT could be first-order (FO) in many new physics models beyond the SM (BSM), such as the real singlet extended SM (xSM) [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, two-Higgs-doublet model [21]}, [22]}, [23]}, [24]}, [25]}, [26]}, [27]}, [28]}, [29]}, [30]}, [31]}, [32]}, [33]}, [34]}, left-right symmetric model [35]}, [36]}A research for the Pati-Salam model can be found in Ref. [37]}., Georgi-Machacek model [38]} and composite Higgs models [39]}, [40]}, [41]}, [42]}, [43]}, [44]}, [45]}, [46]}, etc. A FOEWPT can drive the early Universe out of thermal equilibrium, providing the essential environment for the electroweak baryogenesis (EWBG) mechanism [47]}, [48]}, [49]}, which explains the observed cosmological matter-antimatter asymmetry.
